It is some kind of thin, green cloth-like material, quite fragile. Kinda reminds me of the combat leadership tabs. Is that star even US?

Since these items have been identified as mostly Belgian,this 6 pointed star is I believe a remnant of a Belgian Army officers collar rank badge, the Green was color of several units, Chasseurs a Pied, Chasseurs De Ardennes, Carabiniers, and the Pharmacy Department.